Scala analysis: 605_T12
Aristoxenian style tetrachord 8/3 + 16/3 + 22, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44.444 cents 44.444440 2: 133.333 cents 133.333330 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 366.6667 cents 366.6667 1: 44.4444 cents 44.4444 2: 88.8889 cents 88.8889 3: 366.6667 cents 366.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 44.44444 cents 1: 1 88.88889 cents 1: 1 366.66667 cents 2: 1 133.33333 cents 2: 1 411.11111 cents 2: 1 455.55556 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 44.4 133.3 500.0 44.4 : 88.9 455.6 500.0 133.3: 366.7 411.1 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.4444 .. 366.6667 cents 322.22223 cents 44.44444 cents 2: 133.3333 .. 455.5556 cents 322.22223 cents -233.33334 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 44.44444 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 366.66667 cents Average / Smallest step : 3.750000 Largest / Average step : 2.200000 Largest / Smallest step : 8.250001 Median interval of one step : 88.88889 cents, amount: 1 Least squares average step : 129.36508 cents, oct.: 388.09524 cents Scale is not proper Scale has trivalence property Scale is a mode of a 45-tone equal temperament with octave 500.000 cents degrees: 4 12 45 Least number of segments generator : 23 of 255.556 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 41 of 455.556 cents and inv. generated superset size: 4 = 1 more = 133.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 44.44444 cents Scale diversity : 0.627733 Lumma stability : 0.177778 Lumma impropriety factor : 0.466667 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 44.44444 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 32.0750 c. M: 44.4444 c. 4: 0 1 3 N G T3 SD: 26.1072 c. M: 44.4444 c. 7: 1 1 5 N M DE S SD: 16.5212 c. M:-26.9841 c. 8: 1 1 6 N M DE S SD: 11.4811 c. M:-18.0556 c. 10: 1 2 7 N T3 SD: 10.1430 c. M:-16.6667 c. 11: 1 2 8 N T3 SD: 1.8442 c. M:-3.0303 c. 23: 2 4 17 N T3 SD: 1.7640 c. M: 2.8985 c. 34: 3 6 25 N T3 SD: 0.5966 c. M: 0.9804 c. 45: 4 8 33 N T3 SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 700.0000 cents 2 x x 3 S SD: 201.9550 cents 3 x x 4 S SD: 1.9550 cents 4 x x 5 S SD: 113.6863 cents 5 x 6:7 S SD: 100.0556 cents 6 x 7:8 S SD: 66.7759 cents 7 x 8:9 S SD: 58.7088 cents 8 x 9:11 SD: 43.6308 cents 9 x 10:12 S SD: 24.5547 cents 10 x 11:13 SD: 27.8362 cents 11 x 12:15 S SD: 20.4008 cents 12 x 13:16 SD: 2.7961 cents 13 x 14:17 SD: 17.9634 cents 14 x 15:19 SD: 15.9366 cents 15 x 16:20 S SD: 10.8452 cents 16 x 17:21 SD: 20.3658 cents 17 x 18:23 SD: 20.7706 cents 18 x 19:24 SD: 19.8892 cents 20:21:22:27 SD: 18.2182 cents 21:22:23:28 SD: 14.4922 cents 22:23:24:29 SD: 14.2560 cents 23:24:25:31 SD: 11.8187 cents 24:25:26:32 SD: 8.9392 cents 26:27:28:35 S SD: 8.6627 cents 27:28:29:36 SD: 6.9861 cents 33:34:36:44 SD: 6.2861 cents 35:36:38:47 SD: 4.8064 cents 36:37:39:48 SD: 2.1137 cents 39:40:42:52 SD: 1.8120 cents 74:76:80:99 SD: 1.5179 cents 75:77:81:100 SD: 0.7512 cents 113:116:122:151 SD: 0.7290 cents 149:153:161:199 SD: 0.6232 cents 188:193:203:251 SD: 0.3808 cents 263:270:284:351 SD: 0.3765 cents 275:282:297:367 SD: 0.3361 cents 311:319:336:415 SD: 0.3011 cents 349:358:377:466 SD: 0.2313 cents 388:398:419:518 SD: 0.1813 cents 424:435:458:566 SD: 0.0821 cents